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                            <b>1.</b>
                        
                        第一章：数据分析前奏
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                            <b>1.1.</b>
                        
                        第1节：什么是数据分析
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                            <b>1.2.</b>
                        
                        第2节：环境搭建
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                            <b>1.3.</b>
                        
                        第3节：jupyternotebook使用
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                            <b>1.4.</b>
                        
                        第4节：作业
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                            <b>2.</b>
                        
                        第二章：Numpy库
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                            <b>2.1.</b>
                        
                        第1节：numpy库介绍
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                            <b>2.2.</b>
                        
                        第2节：numpy数组基本
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                            <b>2.3.</b>
                        
                        第3节：numpy数组操作
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                            <b>2.4.</b>
                        
                        第4节：numpy索引和切片
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                            <b>2.5.</b>
                        
                        第5节：Numpy索引和切片作业
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                            <b>2.6.</b>
                        
                        第6节：numpy数组操作
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                            <b>2.7.</b>
                        
                        第7节：深拷贝和浅拷贝
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                            <b>2.8.</b>
                        
                        第8节：文件操作
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                            <b>2.9.</b>
                        
                        第9节：数组操作和文件操作作业.md
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                            <b>2.10.</b>
                        
                        第10节：NAN和INF值处理.md
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                            <b>2.11.</b>
                        
                        第11节：random模块.md
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                            <b>2.12.</b>
                        
                        第12节：axis理解.md
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                            <b>2.13.</b>
                        
                        第13节：通用函数.md
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                            <b>2.14.</b>
                        
                        第14节：numpy练习题.md
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                            <b>3.</b>
                        
                        第三章：Pandas库
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                            <b>3.1.</b>
                        
                        第1节：pandas介绍
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                            <b>3.2.</b>
                        
                        第2节：pandas索引操作
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                            <b>3.3.</b>
                        
                        第3节：pandas对齐运算
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                            <b>3.4.</b>
                        
                        第4节：pandas函数应用
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                            <b>3.5.</b>
                        
                        第5节：pandas层级索引
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                            <b>3.6.</b>
                        
                        第6节：pandas统计计算和描述
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                            <b>3.7.</b>
                        
                        第7节：文件操作
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                            <b>3.8.</b>
                        
                        第8节：数据清洗
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                            <b>3.9.</b>
                        
                        第9节：聚合和分组
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                            <b>3.10.</b>
                        
                        第10节：时间序列
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                            <b>4.</b>
                        
                        第四章：Matploblib库
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                            <b>4.1.</b>
                        
                        第1节：常用图
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                            <b>4.2.</b>
                        
                        第2节：基本使用
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                            <b>4.3.</b>
                        
                        第3节：条形图
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                            <b>4.4.</b>
                        
                        第4节：直方图
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                            <b>4.5.</b>
                        
                        第5节：散点图
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                            <b>4.6.</b>
                        
                        第6节：饼图
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                            <b>4.7.</b>
                        
                        第7节：箱线图
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                            <b>4.8.</b>
                        
                        第8节：雷达图
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                            <b>4.9.</b>
                        
                        第9节：matplotlib绘图分析
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                            <b>4.10.</b>
                        
                        第10节：多图布局
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                            <b>4.11.</b>
                        
                        第11节：matplotlib配置
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                            <b>4.12.</b>
                        
                        第12节：matplotlib作业
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                            <b>5.</b>
                        
                        第五章：Seaborn库
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                            <b>5.1.</b>
                        
                        第1节：关系绘图
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                            <b>5.2.</b>
                        
                        第2节：分类绘图
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                            <b>5.3.</b>
                        
                        第3节：分布绘图
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                            <b>5.4.</b>
                        
                        第4节：线性关系绘图
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                            <b>5.5.</b>
                        
                        第5节：FacetGrid结构图
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                            <b>5.6.</b>
                        
                        第6节：样式设置
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                            <b>5.7.</b>
                        
                        第7节：调色盘设置
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                            <b>5.8.</b>
                        
                        第8节：seaborn作业
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                            <b>6.</b>
                        
                        第六章：统计分析强化
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                            <b>6.1.</b>
                        
                        第1节：常用专业数学术语
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                            <b>6.2.</b>
                        
                        第2节：平均数
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                            <b>6.3.</b>
                        
                        第3节：方差和标准差
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                            <b>6.4.</b>
                        
                        第4节：正态分布
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                            <b>6.5.</b>
                        
                        第5节：对比分析
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        <li class="chapter " data-level="6.6" data-path="chapter3/06分布分析.html">
            
                
                    <a href="../chapter3/06分布分析.html">
                
                        <i class="fa fa-check"></i>
                        
                            <b>6.6.</b>
                        
                        第6节：分布分析
                    </a>
            
            
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        <li class="chapter " data-level="6.7" data-path="chapter3/07交叉分析.html">
            
                
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                            <b>6.7.</b>
                        
                        第7节：交叉分析
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                            <b>6.8.</b>
                        
                        第8节：统计分析
                    </a>
            
            
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                            <b>6.9.</b>
                        
                        第9节：帕累托分析
                    </a>
            
            
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        <li class="chapter " data-level="6.10" data-path="chapter3/10矩阵关联分析.html">
            
                
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                            <b>6.10.</b>
                        
                        第10节：矩阵关联分析
                    </a>
            
            
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        <li class="chapter " data-level="6.11" data-path="chapter3/11综合性分析.html">
            
                
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                        <i class="fa fa-check"></i>
                        
                            <b>6.11.</b>
                        
                        第11节：综合性分析
                    </a>
            
            
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            </ul>
            
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                            <b>7.</b>
                        
                        第七章：数据分析实战
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                            <b>7.1.</b>
                        
                        第1节：App数据分析实战
                    </a>
            
            
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                            <b>7.2.</b>
                        
                        第2节：心脏病患者数据分析
                    </a>
            
            
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        <li class="chapter " data-level="7.3" data-path="chapter6/03StackoverFlow数据分析.html">
            
                
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                            <b>7.3.</b>
                        
                        第3节：StackoverFlow数据分析
                    </a>
            
            
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                            <b>7.4.</b>
                        
                        第4节：二手房数据分析
                    </a>
            
            
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        <li class="chapter " data-level="7.5" data-path="chapter6/05吃鸡数据分析.html">
            
                
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                        <i class="fa fa-check"></i>
                        
                            <b>7.5.</b>
                        
                        第5节：吃鸡数据分析
                    </a>
            
            
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        <li class="chapter " data-level="7.6" data-path="chapter6/06黑色星期五数据分析.html">
            
                
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                            <b>7.6.</b>
                        
                        第6节：黑色星期五数据分析
                    </a>
            
            
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                            <b>8.</b>
                        
                        第八章：补充
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                            <b>8.1.</b>
                        
                        第1节：用Excel做数据分析
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                            <b>8.2.</b>
                        
                        第2节：echarts和pyecharts库
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                            <b>8.3.</b>
                        
                        第3节：bokeh库
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                        <h1 id="numpy&#x6570;&#x7EC4;&#x64CD;&#x4F5C;">Numpy&#x6570;&#x7EC4;&#x64CD;&#x4F5C;</h1>
<h2 id="&#x6570;&#x7EC4;&#x5E7F;&#x64AD;&#x673A;&#x5236;&#xFF1A;">&#x6570;&#x7EC4;&#x5E7F;&#x64AD;&#x673A;&#x5236;&#xFF1A;</h2>
<h3 id="&#x6570;&#x7EC4;&#x4E0E;&#x6570;&#x7684;&#x8BA1;&#x7B97;&#xFF1A;">&#x6570;&#x7EC4;&#x4E0E;&#x6570;&#x7684;&#x8BA1;&#x7B97;&#xFF1A;</h3>
<p>&#x5728;<code>Python</code>&#x5217;&#x8868;&#x4E2D;&#xFF0C;&#x60F3;&#x8981;&#x5BF9;&#x5217;&#x8868;&#x4E2D;&#x6240;&#x6709;&#x7684;&#x5143;&#x7D20;&#x90FD;&#x52A0;&#x4E00;&#x4E2A;&#x6570;&#xFF0C;&#x8981;&#x4E48;&#x91C7;&#x7528;<code>map</code>&#x51FD;&#x6570;&#xFF0C;&#x8981;&#x4E48;&#x5FAA;&#x73AF;&#x6574;&#x4E2A;&#x5217;&#x8868;&#x8FDB;&#x884C;&#x64CD;&#x4F5C;&#x3002;&#x4F46;&#x662F;<code>NumPy</code>&#x4E2D;&#x7684;&#x6570;&#x7EC4;&#x53EF;&#x4EE5;&#x76F4;&#x63A5;&#x5728;&#x6570;&#x7EC4;&#x4E0A;&#x8FDB;&#x884C;&#x64CD;&#x4F5C;&#x3002;&#x793A;&#x4F8B;&#x4EE3;&#x7801;&#x5982;&#x4E0B;&#xFF1A;</p>
<pre><code class="lang-python"><span class="hljs-keyword">import</span> numpy <span class="hljs-keyword">as</span> np
a1 = np.random.random((<span class="hljs-number">3</span>,<span class="hljs-number">4</span>))
print(a1)
<span class="hljs-comment"># &#x5982;&#x679C;&#x60F3;&#x8981;&#x5728;a1&#x6570;&#x7EC4;&#x4E0A;&#x6240;&#x6709;&#x5143;&#x7D20;&#x90FD;&#x4E58;&#x4EE5;10&#xFF0C;&#x90A3;&#x4E48;&#x53EF;&#x4EE5;&#x901A;&#x8FC7;&#x4EE5;&#x4E0B;&#x6765;&#x5B9E;&#x73B0;</span>
a2 = a1*<span class="hljs-number">10</span>
print(a2)
<span class="hljs-comment"># &#x4E5F;&#x53EF;&#x4EE5;&#x4F7F;&#x7528;round&#x8BA9;&#x6240;&#x6709;&#x7684;&#x5143;&#x7D20;&#x53EA;&#x4FDD;&#x7559;2&#x4F4D;&#x5C0F;&#x6570;</span>
a3 = a2.round(<span class="hljs-number">2</span>)
</code></pre>
<p>&#x4EE5;&#x4E0A;&#x4F8B;&#x5B50;&#x662F;&#x76F8;&#x4E58;&#xFF0C;&#x5176;&#x5B9E;&#x76F8;&#x52A0;&#x3001;&#x76F8;&#x51CF;&#x3001;&#x76F8;&#x9664;&#x4E5F;&#x90FD;&#x662F;&#x7C7B;&#x4F3C;&#x7684;&#x3002;</p>
<h3 id="&#x6570;&#x7EC4;&#x4E0E;&#x6570;&#x7EC4;&#x7684;&#x8BA1;&#x7B97;&#xFF1A;">&#x6570;&#x7EC4;&#x4E0E;&#x6570;&#x7EC4;&#x7684;&#x8BA1;&#x7B97;&#xFF1A;</h3>
<ol>
<li><p>&#x7ED3;&#x6784;&#x76F8;&#x540C;&#x7684;&#x6570;&#x7EC4;&#x4E4B;&#x95F4;&#x7684;&#x8FD0;&#x7B97;&#xFF1A;</p>
<pre><code class="lang-python">a1 = np.arange(<span class="hljs-number">0</span>,<span class="hljs-number">24</span>).reshape((<span class="hljs-number">3</span>,<span class="hljs-number">8</span>))
a2 = np.random.randint(<span class="hljs-number">1</span>,<span class="hljs-number">10</span>,size=(<span class="hljs-number">3</span>,<span class="hljs-number">8</span>))
a3 = a1 + a2 <span class="hljs-comment">#&#x76F8;&#x51CF;/&#x76F8;&#x9664;/&#x76F8;&#x4E58;&#x90FD;&#x662F;&#x53EF;&#x4EE5;&#x7684;</span>
print(a1)
print(a2)
print(a3)
</code></pre>
</li>
<li><p>&#x4E0E;&#x884C;&#x6570;&#x76F8;&#x540C;&#x5E76;&#x4E14;&#x53EA;&#x6709;1&#x5217;&#x7684;&#x6570;&#x7EC4;&#x4E4B;&#x95F4;&#x7684;&#x8FD0;&#x7B97;&#xFF1A;</p>
<pre><code class="lang-python">a1 = np.random.randint(<span class="hljs-number">10</span>,<span class="hljs-number">20</span>,size=(<span class="hljs-number">3</span>,<span class="hljs-number">8</span>)) <span class="hljs-comment">#3&#x884C;8&#x5217;</span>
a2 = np.random.randint(<span class="hljs-number">1</span>,<span class="hljs-number">10</span>,size=(<span class="hljs-number">3</span>,<span class="hljs-number">1</span>)) <span class="hljs-comment">#3&#x884C;1&#x5217;</span>
a3 = a1 - a2 <span class="hljs-comment">#&#x884C;&#x6570;&#x76F8;&#x540C;&#xFF0C;&#x4E14;a2&#x53EA;&#x6709;1&#x5217;&#xFF0C;&#x80FD;&#x4E92;&#x76F8;&#x8FD0;&#x7B97;</span>
print(a3)
</code></pre>
</li>
<li><p>&#x4E0E;&#x5217;&#x6570;&#x76F8;&#x540C;&#x5E76;&#x4E14;&#x53EA;&#x6709;1&#x884C;&#x7684;&#x6570;&#x7EC4;&#x4E4B;&#x95F4;&#x7684;&#x8FD0;&#x7B97;&#xFF1A;</p>
<pre><code class="lang-python">a1 = np.random.randint(<span class="hljs-number">10</span>,<span class="hljs-number">20</span>,size=(<span class="hljs-number">3</span>,<span class="hljs-number">8</span>)) <span class="hljs-comment">#3&#x884C;8&#x5217;</span>
a2 = np.random.randint(<span class="hljs-number">1</span>,<span class="hljs-number">10</span>,size=(<span class="hljs-number">1</span>,<span class="hljs-number">8</span>))
a3 = a1 - a2
print(a3)
</code></pre>
</li>
</ol>
<h3 id="&#x5E7F;&#x64AD;&#x539F;&#x5219;&#xFF1A;">&#x5E7F;&#x64AD;&#x539F;&#x5219;&#xFF1A;</h3>
<p><strong>&#x5982;&#x679C;&#x4E24;&#x4E2A;&#x6570;&#x7EC4;&#x7684;&#x540E;&#x7F18;&#x7EF4;&#x5EA6;&#xFF08;trailing dimension&#xFF0C;&#x5373;&#x4ECE;&#x672B;&#x5C3E;&#x5F00;&#x59CB;&#x7B97;&#x8D77;&#x7684;&#x7EF4;&#x5EA6;&#xFF09;&#x7684;&#x8F74;&#x957F;&#x5EA6;&#x76F8;&#x7B26;&#x6216;&#x5176;&#x4E2D;&#x4E00;&#x65B9;&#x7684;&#x957F;&#x5EA6;&#x4E3A;1&#xFF0C;&#x5219;&#x8BA4;&#x4E3A;&#x4ED6;&#x4EEC;&#x662F;&#x5E7F;&#x64AD;&#x517C;&#x5BB9;&#x7684;&#x3002;&#x5E7F;&#x64AD;&#x4F1A;&#x5728;&#x7F3A;&#x5931;&#x548C;&#xFF08;&#x6216;&#xFF09;&#x957F;&#x5EA6;&#x4E3A;1&#x7684;&#x7EF4;&#x5EA6;&#x4E0A;&#x8FDB;&#x884C;&#x3002;</strong>&#x3002;&#x770B;&#x4EE5;&#x4E0B;&#x6848;&#x4F8B;&#x5206;&#x6790;&#xFF1A;</p>
<ol>
<li><p><code>shape</code>&#x4E3A;<code>(3,8,2)</code>&#x7684;&#x6570;&#x7EC4;&#x80FD;&#x548C;<code>(8,3)</code>&#x7684;&#x6570;&#x7EC4;&#x8FDB;&#x884C;&#x8FD0;&#x7B97;&#x5417;&#xFF1F;<br>&#x5206;&#x6790;&#xFF1A;&#x4E0D;&#x80FD;&#xFF0C;&#x56E0;&#x4E3A;&#x6309;&#x7167;&#x5E7F;&#x64AD;&#x539F;&#x5219;&#xFF0C;&#x4ECE;&#x540E;&#x9762;&#x5F80;&#x524D;&#x9762;&#x6570;&#xFF0C;<code>(3,8,2)</code>&#x548C;<code>(8,3)</code>&#x4E2D;&#x7684;<code>2</code>&#x548C;<code>3</code>&#x4E0D;&#x76F8;&#x7B49;&#xFF0C;&#x6240;&#x4EE5;&#x4E0D;&#x80FD;&#x8FDB;&#x884C;&#x8FD0;&#x7B97;&#x3002;</p>
</li>
<li><p><code>shape</code>&#x4E3A;<code>(3,8,2)</code>&#x7684;&#x6570;&#x7EC4;&#x80FD;&#x548C;<code>(8,1)</code>&#x7684;&#x6570;&#x7EC4;&#x8FDB;&#x884C;&#x8FD0;&#x7B97;&#x5417;&#xFF1F;<br>&#x5206;&#x6790;&#xFF1A;&#x80FD;&#xFF0C;&#x56E0;&#x4E3A;&#x6309;&#x7167;&#x5E7F;&#x64AD;&#x539F;&#x5219;&#xFF0C;&#x4ECE;&#x540E;&#x9762;&#x5F80;&#x524D;&#x9762;&#x6570;&#xFF0C;<code>(3,8,2)</code>&#x548C;<code>(8,1)</code>&#x4E2D;&#x7684;<code>2</code>&#x548C;<code>1</code>&#x867D;&#x7136;&#x4E0D;&#x76F8;&#x7B49;&#xFF0C;&#x4F46;&#x662F;&#x56E0;&#x4E3A;&#x6709;&#x4E00;&#x65B9;&#x7684;&#x957F;&#x5EA6;&#x4E3A;<code>1</code>&#xFF0C;&#x6240;&#x4EE5;&#x80FD;&#x53C2;&#x4E0E;&#x8FD0;&#x7B97;&#x3002;</p>
</li>
<li><p><code>shape</code>&#x4E3A;<code>(3,1,8)</code>&#x7684;&#x6570;&#x7EC4;&#x80FD;&#x548C;<code>(8,1)</code>&#x7684;&#x6570;&#x7EC4;&#x8FDB;&#x884C;&#x8FD0;&#x7B97;&#x5417;&#xFF1F;<br>&#x5206;&#x6790;&#xFF1A;&#x80FD;&#xFF0C;&#x56E0;&#x4E3A;&#x6309;&#x7167;&#x5E7F;&#x64AD;&#x539F;&#x5219;&#xFF0C;&#x4ECE;&#x540E;&#x9762;&#x5F80;&#x524D;&#x9762;&#x6570;&#xFF0C;<code>(3,1,4)</code>&#x548C;<code>(8,1)</code>&#x4E2D;&#x7684;<code>4</code>&#x548C;<code>1</code>&#x867D;&#x7136;&#x4E0D;&#x76F8;&#x7B49;&#x4E14;<code>1</code>&#x548C;<code>8</code>&#x4E0D;&#x76F8;&#x7B49;&#xFF0C;&#x4F46;&#x662F;&#x56E0;&#x4E3A;&#x8FD9;&#x4E24;&#x9879;&#x4E2D;&#x6709;&#x4E00;&#x65B9;&#x7684;&#x957F;&#x5EA6;&#x4E3A;<code>1</code>&#xFF0C;&#x6240;&#x4EE5;&#x80FD;&#x53C2;&#x4E0E;&#x8FD0;&#x7B97;&#x3002;</p>
</li>
</ol>
<hr>
<h2 id="&#x6570;&#x7EC4;&#x5F62;&#x72B6;&#x7684;&#x64CD;&#x4F5C;&#xFF1A;">&#x6570;&#x7EC4;&#x5F62;&#x72B6;&#x7684;&#x64CD;&#x4F5C;&#xFF1A;</h2>
<p>&#x53EF;&#x4EE5;&#x901A;&#x8FC7;&#x4E00;&#x4E9B;&#x51FD;&#x6570;&#xFF0C;&#x975E;&#x5E38;&#x65B9;&#x4FBF;&#x7684;&#x64CD;&#x4F5C;&#x6570;&#x7EC4;&#x7684;&#x5F62;&#x72B6;&#x3002;</p>
<h3 id="reshape&#x548C;resize&#x65B9;&#x6CD5;&#xFF1A;">reshape&#x548C;resize&#x65B9;&#x6CD5;&#xFF1A;</h3>
<p>&#x4E24;&#x4E2A;&#x65B9;&#x6CD5;&#x90FD;&#x662F;&#x7528;&#x6765;&#x4FEE;&#x6539;&#x6570;&#x7EC4;&#x5F62;&#x72B6;&#x7684;&#xFF0C;&#x4F46;&#x662F;&#x6709;&#x4E00;&#x4E9B;&#x4E0D;&#x540C;&#x3002;</p>
<ol>
<li><p><code>reshape</code>&#x662F;&#x5C06;&#x6570;&#x7EC4;&#x8F6C;&#x6362;&#x6210;&#x6307;&#x5B9A;&#x7684;&#x5F62;&#x72B6;&#xFF0C;&#x7136;&#x540E;&#x8FD4;&#x56DE;&#x8F6C;&#x6362;&#x540E;&#x7684;&#x7ED3;&#x679C;&#xFF0C;&#x5BF9;&#x4E8E;&#x539F;&#x6570;&#x7EC4;&#x7684;&#x5F62;&#x72B6;&#x662F;&#x4E0D;&#x4F1A;&#x53D1;&#x751F;&#x6539;&#x53D8;&#x7684;&#x3002;&#x8C03;&#x7528;&#x65B9;&#x5F0F;&#xFF1A;</p>
<pre><code class="lang-python">a1 = np.random.randint(<span class="hljs-number">0</span>,<span class="hljs-number">10</span>,size=(<span class="hljs-number">3</span>,<span class="hljs-number">4</span>))
a2 = a1.reshape((<span class="hljs-number">2</span>,<span class="hljs-number">6</span>)) <span class="hljs-comment">#&#x5C06;&#x4FEE;&#x6539;&#x540E;&#x7684;&#x7ED3;&#x679C;&#x8FD4;&#x56DE;&#xFF0C;&#x4E0D;&#x4F1A;&#x5F71;&#x54CD;&#x539F;&#x6570;&#x7EC4;&#x672C;&#x8EAB;</span>
</code></pre>
</li>
<li><p><code>resize</code>&#x662F;&#x5C06;&#x6570;&#x7EC4;&#x8F6C;&#x6362;&#x6210;&#x6307;&#x5B9A;&#x7684;&#x5F62;&#x72B6;&#xFF0C;&#x4F1A;&#x76F4;&#x63A5;&#x4FEE;&#x6539;&#x6570;&#x7EC4;&#x672C;&#x8EAB;&#x3002;&#x5E76;&#x4E0D;&#x4F1A;&#x8FD4;&#x56DE;&#x4EFB;&#x4F55;&#x503C;&#x3002;&#x8C03;&#x7528;&#x65B9;&#x5F0F;&#xFF1A;</p>
<pre><code class="lang-python">a1 = np.random.randint(<span class="hljs-number">0</span>,<span class="hljs-number">10</span>,size=(<span class="hljs-number">3</span>,<span class="hljs-number">4</span>))
a1.resize((<span class="hljs-number">2</span>,<span class="hljs-number">6</span>)) <span class="hljs-comment">#a1&#x672C;&#x8EAB;&#x53D1;&#x751F;&#x4E86;&#x6539;&#x53D8;</span>
</code></pre>
</li>
</ol>
<h3 id="flatten&#x548C;ravel&#x65B9;&#x6CD5;&#xFF1A;">flatten&#x548C;ravel&#x65B9;&#x6CD5;&#xFF1A;</h3>
<p>&#x4E24;&#x4E2A;&#x65B9;&#x6CD5;&#x90FD;&#x662F;&#x5C06;&#x591A;&#x7EF4;&#x6570;&#x7EC4;&#x8F6C;&#x6362;&#x4E3A;&#x4E00;&#x7EF4;&#x6570;&#x7EC4;&#xFF0C;&#x4F46;&#x662F;&#x6709;&#x4EE5;&#x4E0B;&#x4E0D;&#x540C;&#xFF1A;  </p>
<ol>
<li><code>flatten</code>&#x662F;&#x5C06;&#x6570;&#x7EC4;&#x8F6C;&#x6362;&#x4E3A;&#x4E00;&#x7EF4;&#x6570;&#x7EC4;&#x540E;&#xFF0C;&#x7136;&#x540E;&#x5C06;&#x8FD9;&#x4E2A;&#x62F7;&#x8D1D;&#x8FD4;&#x56DE;&#x56DE;&#x53BB;&#xFF0C;&#x6240;&#x4EE5;&#x540E;&#x7EED;&#x5BF9;&#x8FD9;&#x4E2A;&#x8FD4;&#x56DE;&#x503C;&#x8FDB;&#x884C;&#x4FEE;&#x6539;&#x4E0D;&#x4F1A;&#x5F71;&#x54CD;&#x4E4B;&#x524D;&#x7684;&#x6570;&#x7EC4;&#x3002;  </li>
<li><code>ravel</code>&#x662F;&#x5C06;&#x6570;&#x7EC4;&#x8F6C;&#x6362;&#x4E3A;&#x4E00;&#x7EF4;&#x6570;&#x7EC4;&#x540E;&#xFF0C;&#x5C06;&#x8FD9;&#x4E2A;&#x89C6;&#x56FE;&#xFF08;&#x53EF;&#x4EE5;&#x7406;&#x89E3;&#x4E3A;&#x5F15;&#x7528;&#xFF09;&#x8FD4;&#x56DE;&#x56DE;&#x53BB;&#xFF0C;&#x6240;&#x4EE5;&#x540E;&#x7EED;&#x5BF9;&#x8FD9;&#x4E2A;&#x8FD4;&#x56DE;&#x503C;&#x8FDB;&#x884C;&#x4FEE;&#x6539;&#x4F1A;&#x5F71;&#x54CD;&#x4E4B;&#x524D;&#x7684;&#x6570;&#x7EC4;&#x3002;<br>&#x6BD4;&#x5982;&#x4EE5;&#x4E0B;&#x4EE3;&#x7801;&#xFF1A;</li>
</ol>
<pre><code class="lang-python">x = np.array([[<span class="hljs-number">1</span>, <span class="hljs-number">2</span>], [<span class="hljs-number">3</span>, <span class="hljs-number">4</span>]])
x.flatten()[<span class="hljs-number">1</span>] = <span class="hljs-number">100</span> <span class="hljs-comment">#&#x6B64;&#x65F6;&#x7684;x[0]&#x7684;&#x4F4D;&#x7F6E;&#x5143;&#x7D20;&#x8FD8;&#x662F;1</span>
x.ravel()[<span class="hljs-number">1</span>] = <span class="hljs-number">100</span> <span class="hljs-comment">#&#x6B64;&#x65F6;x[0]&#x7684;&#x4F4D;&#x7F6E;&#x5143;&#x7D20;&#x662F;100</span>
</code></pre>
<h3 id="&#x4E0D;&#x540C;&#x6570;&#x7EC4;&#x7684;&#x7EC4;&#x5408;&#xFF1A;">&#x4E0D;&#x540C;&#x6570;&#x7EC4;&#x7684;&#x7EC4;&#x5408;&#xFF1A;</h3>
<p>&#x5982;&#x679C;&#x6709;&#x591A;&#x4E2A;&#x6570;&#x7EC4;&#x60F3;&#x8981;&#x7EC4;&#x5408;&#x5728;&#x4E00;&#x8D77;&#xFF0C;&#x4E5F;&#x53EF;&#x4EE5;&#x901A;&#x8FC7;&#x5176;&#x4E2D;&#x7684;&#x4E00;&#x4E9B;&#x51FD;&#x6570;&#x6765;&#x5B9E;&#x73B0;&#x3002;</p>
<ol>
<li><p><code>vstack</code>&#xFF1A;&#x5C06;&#x6570;&#x7EC4;&#x6309;&#x5782;&#x76F4;&#x65B9;&#x5411;&#x8FDB;&#x884C;&#x53E0;&#x52A0;&#x3002;&#x6570;&#x7EC4;&#x7684;&#x5217;&#x6570;&#x5FC5;&#x987B;&#x76F8;&#x540C;&#x624D;&#x80FD;&#x53E0;&#x52A0;&#x3002;&#x793A;&#x4F8B;&#x4EE3;&#x7801;&#x5982;&#x4E0B;&#xFF1A;</p>
<pre><code class="lang-python">a1 = np.random.randint(<span class="hljs-number">0</span>,<span class="hljs-number">10</span>,size=(<span class="hljs-number">3</span>,<span class="hljs-number">5</span>))
a2 = np.random.randint(<span class="hljs-number">0</span>,<span class="hljs-number">10</span>,size=(<span class="hljs-number">1</span>,<span class="hljs-number">5</span>))
a3 = np.vstack([a1,a2])
</code></pre>
</li>
<li><p><code>hstack</code>&#xFF1A;&#x5C06;&#x6570;&#x7EC4;&#x6309;&#x6C34;&#x5E73;&#x65B9;&#x5411;&#x8FDB;&#x884C;&#x53E0;&#x52A0;&#x3002;&#x6570;&#x7EC4;&#x7684;&#x884C;&#x5FC5;&#x987B;&#x76F8;&#x540C;&#x624D;&#x80FD;&#x53E0;&#x52A0;&#x3002;&#x793A;&#x4F8B;&#x4EE3;&#x7801;&#x5982;&#x4E0B;&#xFF1A;</p>
<pre><code class="lang-python">a1 = np.random.randint(<span class="hljs-number">0</span>,<span class="hljs-number">10</span>,size=(<span class="hljs-number">3</span>,<span class="hljs-number">2</span>))
a2 = np.random.randint(<span class="hljs-number">0</span>,<span class="hljs-number">10</span>,size=(<span class="hljs-number">3</span>,<span class="hljs-number">1</span>))
a3 = np.hstack([a1,a2])
</code></pre>
</li>
<li><p><code>concatenate([],axis)</code>&#xFF1A;&#x5C06;&#x4E24;&#x4E2A;&#x6570;&#x7EC4;&#x8FDB;&#x884C;&#x53E0;&#x52A0;&#xFF0C;&#x4F46;&#x662F;&#x5177;&#x4F53;&#x662F;&#x6309;&#x6C34;&#x5E73;&#x65B9;&#x5411;&#x8FD8;&#x662F;&#x6309;&#x5782;&#x76F4;&#x65B9;&#x5411;&#x3002;&#x5219;&#x8981;&#x770B;<code>axis</code>&#x7684;&#x53C2;&#x6570;&#xFF0C;&#x5982;&#x679C;<code>axis=0</code>&#xFF0C;&#x90A3;&#x4E48;&#x4EE3;&#x8868;&#x7684;&#x662F;&#x5F80;&#x5782;&#x76F4;&#x65B9;&#x5411;&#xFF08;&#x884C;&#xFF09;&#x53E0;&#x52A0;&#xFF0C;&#x5982;&#x679C;<code>axis=1</code>&#xFF0C;&#x90A3;&#x4E48;&#x4EE3;&#x8868;&#x7684;&#x662F;&#x5F80;&#x6C34;&#x5E73;&#x65B9;&#x5411;&#xFF08;&#x5217;&#xFF09;&#x4E0A;&#x53E0;&#x52A0;&#xFF0C;&#x5982;&#x679C;<code>axis=None</code>&#xFF0C;&#x90A3;&#x4E48;&#x4F1A;&#x5C06;&#x4E24;&#x4E2A;&#x6570;&#x7EC4;&#x7EC4;&#x5408;&#x6210;&#x4E00;&#x4E2A;&#x4E00;&#x7EF4;&#x6570;&#x7EC4;&#x3002;&#x9700;&#x8981;&#x6CE8;&#x610F;&#x7684;&#x662F;&#xFF0C;&#x5982;&#x679C;&#x5F80;&#x6C34;&#x5E73;&#x65B9;&#x5411;&#x4E0A;&#x53E0;&#x52A0;&#xFF0C;&#x90A3;&#x4E48;&#x884C;&#x5FC5;&#x987B;&#x76F8;&#x540C;&#xFF0C;&#x5982;&#x679C;&#x662F;&#x5F80;&#x5782;&#x76F4;&#x65B9;&#x5411;&#x53E0;&#x52A0;&#xFF0C;&#x90A3;&#x4E48;&#x5217;&#x5FC5;&#x987B;&#x76F8;&#x540C;&#x3002;&#x793A;&#x4F8B;&#x4EE3;&#x7801;&#x5982;&#x4E0B;&#xFF1A;</p>
<pre><code class="lang-python">a = np.array([[<span class="hljs-number">1</span>, <span class="hljs-number">2</span>], [<span class="hljs-number">3</span>, <span class="hljs-number">4</span>]])
b = np.array([[<span class="hljs-number">5</span>, <span class="hljs-number">6</span>]])
np.concatenate((a, b), axis=<span class="hljs-number">0</span>)
<span class="hljs-comment"># &#x7ED3;&#x679C;&#xFF1A;</span>
array([[<span class="hljs-number">1</span>, <span class="hljs-number">2</span>],
    [<span class="hljs-number">3</span>, <span class="hljs-number">4</span>],
    [<span class="hljs-number">5</span>, <span class="hljs-number">6</span>]])

np.concatenate((a, b.T), axis=<span class="hljs-number">1</span>)
<span class="hljs-comment"># &#x7ED3;&#x679C;&#xFF1A;</span>
array([[<span class="hljs-number">1</span>, <span class="hljs-number">2</span>, <span class="hljs-number">5</span>],
    [<span class="hljs-number">3</span>, <span class="hljs-number">4</span>, <span class="hljs-number">6</span>]])

np.concatenate((a, b), axis=<span class="hljs-keyword">None</span>)
<span class="hljs-comment"># &#x7ED3;&#x679C;&#xFF1A;</span>
array([<span class="hljs-number">1</span>, <span class="hljs-number">2</span>, <span class="hljs-number">3</span>, <span class="hljs-number">4</span>, <span class="hljs-number">5</span>, <span class="hljs-number">6</span>])
</code></pre>
</li>
</ol>
<h3 id="&#x6570;&#x7EC4;&#x7684;&#x5207;&#x5272;&#xFF1A;">&#x6570;&#x7EC4;&#x7684;&#x5207;&#x5272;&#xFF1A;</h3>
<p>&#x901A;&#x8FC7;<code>hsplit</code>&#x548C;<code>vsplit</code>&#x4EE5;&#x53CA;<code>array_split</code>&#x53EF;&#x4EE5;&#x5C06;&#x4E00;&#x4E2A;&#x6570;&#x7EC4;&#x8FDB;&#x884C;&#x5207;&#x5272;&#x3002;</p>
<ol>
<li><p><code>hsplit</code>&#xFF1A;&#x6309;&#x7167;&#x6C34;&#x5E73;&#x65B9;&#x5411;&#x8FDB;&#x884C;&#x5207;&#x5272;&#x3002;&#x7528;&#x4E8E;&#x6307;&#x5B9A;&#x5206;&#x5272;&#x6210;&#x51E0;&#x5217;&#xFF0C;&#x53EF;&#x4EE5;&#x4F7F;&#x7528;&#x6570;&#x5B57;&#x6765;&#x4EE3;&#x8868;&#x5206;&#x6210;&#x51E0;&#x90E8;&#x5206;&#xFF0C;&#x4E5F;&#x53EF;&#x4EE5;&#x4F7F;&#x7528;&#x6570;&#x7EC4;&#x6765;&#x4EE3;&#x8868;&#x5206;&#x5272;&#x7684;&#x5730;&#x65B9;&#x3002;&#x793A;&#x4F8B;&#x4EE3;&#x7801;&#x5982;&#x4E0B;&#xFF1A;</p>
<pre><code class="lang-python">a1 = np.arange(<span class="hljs-number">16.0</span>).reshape(<span class="hljs-number">4</span>, <span class="hljs-number">4</span>)
np.hsplit(a1,<span class="hljs-number">2</span>) <span class="hljs-comment">#&#x5206;&#x5272;&#x6210;&#x4E24;&#x90E8;&#x5206;</span>
<span class="hljs-prompt">&gt;&gt;&gt; </span>array([[ <span class="hljs-number">0.</span>,  <span class="hljs-number">1.</span>],
     [ <span class="hljs-number">4.</span>,  <span class="hljs-number">5.</span>],
     [ <span class="hljs-number">8.</span>,  <span class="hljs-number">9.</span>],
     [<span class="hljs-number">12.</span>, <span class="hljs-number">13.</span>]]), array([[ <span class="hljs-number">2.</span>,  <span class="hljs-number">3.</span>],
     [ <span class="hljs-number">6.</span>,  <span class="hljs-number">7.</span>],
     [<span class="hljs-number">10.</span>, <span class="hljs-number">11.</span>],
     [<span class="hljs-number">14.</span>, <span class="hljs-number">15.</span>]])]

np.hsplit(a1,[<span class="hljs-number">1</span>,<span class="hljs-number">2</span>]) <span class="hljs-comment">#&#x4EE3;&#x8868;&#x5728;&#x4E0B;&#x6807;&#x4E3A;1&#x7684;&#x5730;&#x65B9;&#x5207;&#x4E00;&#x5200;&#xFF0C;&#x4E0B;&#x6807;&#x4E3A;2&#x7684;&#x5730;&#x65B9;&#x5207;&#x4E00;&#x5200;&#xFF0C;&#x5206;&#x6210;&#x4E09;&#x90E8;&#x5206;</span>
<span class="hljs-prompt">&gt;&gt;&gt; </span>[array([[ <span class="hljs-number">0.</span>],
     [ <span class="hljs-number">4.</span>],
     [ <span class="hljs-number">8.</span>],
     [<span class="hljs-number">12.</span>]]), array([[ <span class="hljs-number">1.</span>],
     [ <span class="hljs-number">5.</span>],
     [ <span class="hljs-number">9.</span>],
     [<span class="hljs-number">13.</span>]]), array([[ <span class="hljs-number">2.</span>,  <span class="hljs-number">3.</span>],
     [ <span class="hljs-number">6.</span>,  <span class="hljs-number">7.</span>],
     [<span class="hljs-number">10.</span>, <span class="hljs-number">11.</span>],
     [<span class="hljs-number">14.</span>, <span class="hljs-number">15.</span>]])]
</code></pre>
</li>
<li><p><code>vsplit</code>&#xFF1A;&#x6309;&#x7167;&#x5782;&#x76F4;&#x65B9;&#x5411;&#x8FDB;&#x884C;&#x5207;&#x5272;&#x3002;&#x7528;&#x4E8E;&#x6307;&#x5B9A;&#x5206;&#x5272;&#x6210;&#x51E0;&#x884C;&#xFF0C;&#x53EF;&#x4EE5;&#x4F7F;&#x7528;&#x6570;&#x5B57;&#x6765;&#x4EE3;&#x8868;&#x5206;&#x6210;&#x51E0;&#x90E8;&#x5206;&#xFF0C;&#x4E5F;&#x53EF;&#x4EE5;&#x4F7F;&#x7528;&#x6570;&#x7EC4;&#x6765;&#x4EE3;&#x8868;&#x5206;&#x5272;&#x7684;&#x5730;&#x65B9;&#x3002;&#x793A;&#x4F8B;&#x4EE3;&#x7801;&#x5982;&#x4E0B;&#xFF1A;</p>
<pre><code class="lang-python">np.vsplit(x,<span class="hljs-number">2</span>) <span class="hljs-comment">#&#x4EE3;&#x8868;&#x6309;&#x7167;&#x884C;&#x603B;&#x5171;&#x5206;&#x6210;2&#x4E2A;&#x6570;&#x7EC4;</span>
<span class="hljs-prompt">&gt;&gt;&gt; </span>[array([[<span class="hljs-number">0.</span>, <span class="hljs-number">1.</span>, <span class="hljs-number">2.</span>, <span class="hljs-number">3.</span>],
     [<span class="hljs-number">4.</span>, <span class="hljs-number">5.</span>, <span class="hljs-number">6.</span>, <span class="hljs-number">7.</span>]]), array([[ <span class="hljs-number">8.</span>,  <span class="hljs-number">9.</span>, <span class="hljs-number">10.</span>, <span class="hljs-number">11.</span>],
     [<span class="hljs-number">12.</span>, <span class="hljs-number">13.</span>, <span class="hljs-number">14.</span>, <span class="hljs-number">15.</span>]])]

np.vsplit(x,(<span class="hljs-number">1</span>,<span class="hljs-number">2</span>)) <span class="hljs-comment">#&#x4EE3;&#x8868;&#x6309;&#x7167;&#x884C;&#x8FDB;&#x884C;&#x5212;&#x5206;&#xFF0C;&#x5728;&#x4E0B;&#x6807;&#x4E3A;1&#x7684;&#x5730;&#x65B9;&#x548C;&#x4E0B;&#x6807;&#x4E3A;2&#x7684;&#x5730;&#x65B9;&#x5206;&#x5272;</span>
<span class="hljs-prompt">&gt;&gt;&gt; </span>[array([[<span class="hljs-number">0.</span>, <span class="hljs-number">1.</span>, <span class="hljs-number">2.</span>, <span class="hljs-number">3.</span>]]),
    array([[<span class="hljs-number">4.</span>, <span class="hljs-number">5.</span>, <span class="hljs-number">6.</span>, <span class="hljs-number">7.</span>]]),
    array([[ <span class="hljs-number">8.</span>,  <span class="hljs-number">9.</span>, <span class="hljs-number">10.</span>, <span class="hljs-number">11.</span>],
           [<span class="hljs-number">12.</span>, <span class="hljs-number">13.</span>, <span class="hljs-number">14.</span>, <span class="hljs-number">15.</span>]])]
</code></pre>
</li>
<li><p><code>split/array_split(array,indicate_or_seciont,axis)</code>&#xFF1A;&#x7528;&#x4E8E;&#x6307;&#x5B9A;&#x5207;&#x5272;&#x65B9;&#x5F0F;&#xFF0C;&#x5728;&#x5207;&#x5272;&#x7684;&#x65F6;&#x5019;&#x9700;&#x8981;&#x6307;&#x5B9A;&#x662F;&#x6309;&#x7167;&#x884C;&#x8FD8;&#x662F;&#x6309;&#x7167;&#x5217;&#xFF0C;<code>axis=1</code>&#x4EE3;&#x8868;&#x6309;&#x7167;&#x5217;&#xFF0C;<code>axis=0</code>&#x4EE3;&#x8868;&#x6309;&#x7167;&#x884C;&#x3002;&#x793A;&#x4F8B;&#x4EE3;&#x7801;&#x5982;&#x4E0B;&#xFF1A;</p>
<pre><code class="lang-python">np.array_split(x,<span class="hljs-number">2</span>,axis=<span class="hljs-number">0</span>) <span class="hljs-comment">#&#x6309;&#x7167;&#x5782;&#x76F4;&#x65B9;&#x5411;&#x5207;&#x5272;&#x6210;2&#x90E8;&#x5206;</span>
<span class="hljs-prompt">&gt;&gt;&gt; </span>[array([[<span class="hljs-number">0.</span>, <span class="hljs-number">1.</span>, <span class="hljs-number">2.</span>, <span class="hljs-number">3.</span>],
     [<span class="hljs-number">4.</span>, <span class="hljs-number">5.</span>, <span class="hljs-number">6.</span>, <span class="hljs-number">7.</span>]]), array([[ <span class="hljs-number">8.</span>,  <span class="hljs-number">9.</span>, <span class="hljs-number">10.</span>, <span class="hljs-number">11.</span>],
     [<span class="hljs-number">12.</span>, <span class="hljs-number">13.</span>, <span class="hljs-number">14.</span>, <span class="hljs-number">15.</span>]])]
</code></pre>
</li>
</ol>
<hr>
<h2 id="&#x6570;&#x7EC4;&#xFF08;&#x77E9;&#x9635;&#xFF09;&#x8F6C;&#x7F6E;&#x548C;&#x8F74;&#x5BF9;&#x6362;&#xFF1A;">&#x6570;&#x7EC4;&#xFF08;&#x77E9;&#x9635;&#xFF09;&#x8F6C;&#x7F6E;&#x548C;&#x8F74;&#x5BF9;&#x6362;&#xFF1A;</h2>
<p><code>numpy</code>&#x4E2D;&#x7684;&#x6570;&#x7EC4;&#x5176;&#x5B9E;&#x5C31;&#x662F;&#x7EBF;&#x6027;&#x4EE3;&#x6570;&#x4E2D;&#x7684;&#x77E9;&#x9635;&#x3002;&#x77E9;&#x9635;&#x662F;&#x53EF;&#x4EE5;&#x8FDB;&#x884C;&#x8F6C;&#x7F6E;&#x7684;&#x3002;<code>ndarray</code>&#x6709;&#x4E00;&#x4E2A;<code>T</code>&#x5C5E;&#x6027;&#xFF0C;&#x53EF;&#x4EE5;&#x8FD4;&#x56DE;&#x8FD9;&#x4E2A;&#x6570;&#x7EC4;&#x7684;&#x8F6C;&#x7F6E;&#x7684;&#x7ED3;&#x679C;&#x3002;&#x793A;&#x4F8B;&#x4EE3;&#x7801;&#x5982;&#x4E0B;&#xFF1A;</p>
<pre><code class="lang-python">a1 = np.arange(<span class="hljs-number">0</span>,<span class="hljs-number">24</span>).reshape((<span class="hljs-number">4</span>,<span class="hljs-number">6</span>))
a2 = a1.T
print(a2)
</code></pre>
<p>&#x53E6;&#x5916;&#x8FD8;&#x6709;&#x4E00;&#x4E2A;&#x65B9;&#x6CD5;&#x53EB;&#x505A;<code>transpose</code>&#xFF0C;&#x8FD9;&#x4E2A;&#x65B9;&#x6CD5;&#x8FD4;&#x56DE;&#x7684;&#x662F;&#x4E00;&#x4E2A;View&#xFF0C;&#x4E5F;&#x5373;&#x4FEE;&#x6539;&#x8FD4;&#x56DE;&#x503C;&#xFF0C;&#x4F1A;&#x5F71;&#x54CD;&#x5230;&#x539F;&#x6765;&#x6570;&#x7EC4;&#x3002;&#x793A;&#x4F8B;&#x4EE3;&#x7801;&#x5982;&#x4E0B;&#xFF1A;</p>
<pre><code class="lang-python">a1 = np.arange(<span class="hljs-number">0</span>,<span class="hljs-number">24</span>).reshape((<span class="hljs-number">4</span>,<span class="hljs-number">6</span>))
a2 = a1.transpose()
</code></pre>
<p>&#x4E3A;&#x4EC0;&#x4E48;&#x8981;&#x8FDB;&#x884C;&#x77E9;&#x9635;&#x8F6C;&#x7F6E;&#x5462;&#xFF0C;&#x6709;&#x65F6;&#x5019;&#x5728;&#x505A;&#x4E00;&#x4E9B;&#x8BA1;&#x7B97;&#x7684;&#x65F6;&#x5019;&#x9700;&#x8981;&#x7528;&#x5230;&#x3002;&#x6BD4;&#x5982;&#x505A;&#x77E9;&#x9635;&#x7684;&#x5185;&#x79EF;&#x7684;&#x65F6;&#x5019;&#x3002;&#x5C31;&#x5FC5;&#x987B;&#x5C06;&#x77E9;&#x9635;&#x8FDB;&#x884C;&#x8F6C;&#x7F6E;&#x540E;&#x518D;&#x4E58;&#x4EE5;&#x4E4B;&#x524D;&#x7684;&#x77E9;&#x9635;&#xFF1A;</p>
<pre><code class="lang-python">a1 = np.arange(<span class="hljs-number">0</span>,<span class="hljs-number">24</span>).reshape((<span class="hljs-number">4</span>,<span class="hljs-number">6</span>))
a2 = a1.T
print(a1.dot(a2))
</code></pre>

                    
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